asked 2021-09-14

asked 2021-09-07

Find the area of the surface.

The part of the paraboloid

\(\displaystyle{z}={1}−{x}^{{2}}−{y}^{{2}}\)

that lies above the plane

\(\displaystyle{z}=−{6}\)

The part of the paraboloid

\(\displaystyle{z}={1}−{x}^{{2}}−{y}^{{2}}\)

that lies above the plane

\(\displaystyle{z}=−{6}\)

asked 2021-10-26

Find an equation of the tangent plane to the given parametric surface at the specified point. \(\displaystyle{x}={u}^{{{2}}}+{1},{y}={v}^{{{3}}}+{1},{z}={u}+{v};{\left({5},{2},{3}\right)}\)

asked 2021-09-12

Surface s is a part of the paraboloid \(\displaystyle{z}={4}-{x}^{{2}}-{y}^{{2}}\) that lies above the plane \(z=0\).\((6+7+7=20pt)\)

a) Find the parametric equation \(\displaystyle\vec{{r}}{\left({u},{v}\right)}\) of the surface with polar coordinates \(\displaystyle{x}={u}{\cos{{\left({v}\right)}}},{y}={u}{\sin{{\left({v}\right)}}}\) and find the domain D for u and v.

b) Find \(\displaystyle\vec{{r}}_{{u}},\vec{{r}}_{{v}},\) and \(\displaystyle\vec{{r}}_{{u}}\cdot\vec{{r}}_{{v}}\).

c) Find the area of the surface

asked 2021-05-13

Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

asked 2021-11-12

Find a vector-valued function whose graph is the indicated surface.

The cylinder \(\displaystyle{4}{x}^{{2}}+{y}^{{2}}={16}\)

The cylinder \(\displaystyle{4}{x}^{{2}}+{y}^{{2}}={16}\)